总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (d+5)(d+2)(d+3)+d(d+5)(d+3)+d(d+5)(d+2) = d(d+2)(d+3) 的解.
题型:方程
解:原方程:| | ( | d | + | 5 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | d | ( | d | + | 5 | ) | ( | d | + | 3 | ) | + | d | ( | d | + | 5 | ) | ( | d | + | 2 | ) | = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
去掉方程左边的括号:
| 方程左边 = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | 5 | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | d | ( | d | + | 5 | ) | ( | d | + | 3 | ) | + | d | ( | d | + | 5 | ) | ( | d | + | 2 | ) |
| = | d | d | ( | d | + | 3 | ) | + | d | × | 2 | ( | d | + | 3 | ) | + | 5 | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | d | ( | d | + | 5 | ) | ( | d | + | 3 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | ( | d | + | 3 | ) | + | 5 | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | d | × | 2 | × | 3 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | d | × | 6 | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 21 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 21 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 21 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 31 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 31 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 31 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 31 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 31 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 46 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 46 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 46 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 46 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 46 | d | + | 5 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 56 | d | + | 5 |
方程化为:
| | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 56 | d | + | 5 | = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
去掉方程右边的括号:
| 方程右边 = | d | d | ( | d | + | 3 | ) | + | d | × | 2 | ( | d | + | 3 | ) |
方程的解为:
d1≈-6.517113 ,保留6位小数
d2≈-2.596424 ,保留6位小数
d3≈-0.886462 ,保留6位小数
有 3个解。
解程的详细方法请参阅:《方程的解法》
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